Kappa-tau type PI tuning rules for specified robust levels: The frequency response method

New tuning rules for two-degree-of-freedom (2-DoF) PI controllers for several robustness levels in the spirit of the kappa-tau tuning rules are presented in this paper. The rules are based on the characterization of the process dynamics by three parameters, i.e. the static gain K_P, and the gain K₁₈₀ and frequency ω₁₈₀ where the process phase lag is 180^o, which can be determined by a simple manual experiment. In particular, tuning rules have been devised in order to minimize the integrated absolute error with a constraint on the maximum sensitivity M_S. Different tuning rules have been obtained for a batch of plants and for several robustness levels in terms of M_S. The setpoint weight is also exploited to improve the setpoint following performance because the PI controller is tuned by optimizing the load disturbance rejection performance. In particular, explicit tuning rules are given in order to select the optimal setpoint weight to minimize the integrated absolute error. Some comments relating to industrial practice are offered in this context.